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On the last exit times for spectrally negative Lévy processes

Part of: Stochastic processes Special processes

Published online by Cambridge University Press:  22 June 2017

Yingqiu Li ,
Chuancun Yin  and
Xiaowen Zhou
Yingqiu Li*
Affiliation:
Changsha University of Science and Technology
Chuancun Yin*
Affiliation:
Qufu Normal University
Xiaowen Zhou*
Affiliation:
Concordia University
*
* Postal address: School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, China.
** Postal address: School of Statistics, Qufu Normal University, Qufu, Shandong 273165, China.
*** Postal address: Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8, Canada. Email address: [email protected]
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Abstract

Using a new approach, for spectrally negative Lévy processes we find joint Laplace transforms involving the last exit time (from a semiinfinite interval), the value of the process at the last exit time, and the associated occupation time, which generalize some previous results.

Keywords

Spectrally negative Lévy processlast exit timeGerber–Shiu functionoccupation time

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 474 - 489
Copyright
Copyright © Applied Probability Trust 2017 

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